Exact solutions of the (3+1)-dimensional DKP oscillator in doubly special relativity.

Doubly Special Relativity (DSR) is a promising candidate for understanding quantum gravity, by introducing two fundamental invariant scales — the speed of light and the Planck energy. Recently, another such theory has been proposed by Magueijo and Smolin (MS), and it can be extended to the whole class of DSRs. These models have structural similarity with different realizations of κ -Poincaré algebras. Given the significant implications of this theory, we explore the three-dimensional Duffin–Kemmer–Petiau (DKP) oscillator within this framework. By using the vector spherical harmonics technique in the momentum space, the three-dimensional DKP oscillator equation for spins 1 and 0 is reformulated from the viewpoint of the generalized algebra of the MS model. In order to recognize the influence of this reformulation, the energy eigenvalues contain an additional correction which depends on the deformation parameter, and eigenfunctions are determined in terms of the associated Laguerre polynomials. [ABSTRACT FROM AUTHOR]